Original articles

Mathematische Annalen

, Volume 320, Issue 1, pp 167-190

Topological obstructions to nonnegative curvature

  • Igor BelegradekAffiliated withDepartment of Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, USA (e-mail: ibeleg@its.caltech.edu)
  • , Vitali KapovitchAffiliated withDepartment of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA (e-mail: vitali@math.upenn.edu)

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Abstract.

We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit no nonnegatively curved metrics.

Mathematics Subject Classification (1991): 53C20